scholarly journals Constancy regions of mixed multiplier ideals in two-dimensional local rings with rational singularities

2017 ◽  
Vol 291 (2-3) ◽  
pp. 245-263 ◽  
Author(s):  
Maria Alberich-Carramiñana ◽  
Josep Àlvarez Montaner ◽  
Ferran Dachs-Cadefau
Keyword(s):  
Local Rings ◽  
Two Dimensional ◽  
Multiplier Ideals ◽  
Rational Singularities

scholarly journals Multiplier ideals in two-dimensional local rings with rational singularities

2016 ◽  
Vol 65 (2) ◽  
pp. 287-320 ◽  
Author(s):  
Maria Alberich-Carramiñana ◽  
Josep Àlvarez Montaner ◽  
Ferran Dachs-Cadefau
Keyword(s):  
Local Rings ◽  
Two Dimensional ◽  
Multiplier Ideals ◽  
Rational Singularities

scholarly journals Poincaré series of multiplier ideals in two-dimensional local rings with rational singularities

2017 ◽  
Vol 304 ◽  
pp. 769-792 ◽  
Author(s):  
Maria Alberich-Carramiñana ◽  
Josep Àlvarez Montaner ◽  
Ferran Dachs-Cadefau ◽  
Víctor González-Alonso
Keyword(s):  
Poincaré Series ◽  
Local Rings ◽  
Two Dimensional ◽  
Poincare Series ◽  
Multiplier Ideals ◽  
Rational Singularities

Two-Dimensional Linear Groups Over Local Rings

1969 ◽  
Vol 21 ◽  
pp. 106-135 ◽  
Author(s):  
Norbert H. J. Lacroix
Keyword(s):  
Local Ring ◽  
Linear Group ◽  
General Linear Group ◽  
General Linear ◽  
Linear Groups ◽  
Local Rings ◽  
Two Dimensional ◽  
Normal Subgroups ◽  
Field Case

The problem of classifying the normal subgroups of the general linear group over a field was solved in the general case by Dieudonné (see 2 and 3). If we consider the problem over a ring, it is trivial to see that there will be more normal subgroups than in the field case. Klingenberg (4) has investigated the situation over a local ring and has shown that they are classified by certain congruence groups which are determined by the ideals in the ring.Klingenberg's solution roughly goes as follows. To a given ideal , attach certain congruence groups and . Next, assign a certain ideal (called the order) to a given subgroup G. The main result states that if G is normal with order a, then ≧ G ≧ , that is, G satisfies the so-called ladder relation at ; conversely, if G satisfies the ladder relation at , then G is normal and has order .

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